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Free Fall

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Projectile Motion – free fall, but not vertical

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Free Fall : Used to describe the motion of any object that is moving _____________________________ the only force acting is ________________ no _____________________, which is a good approximation if object moves ____________ motion can be _________________ or in an arc known as a ____________________ the results are independent of ___________ All of the equations of __________________can used as long as you use: a = _______ = ___________________= ____________ = _____________on or near Earth’s surface for the time the object is in ________________. gravity air resistance parabola up or down slowly mass 9.81 m/s 2 down -9.81 m/s 2 -g constant kinematics freely through a vacuum. free fall

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Free fall applies to an object that is… ___________ from rest: _______up: fired ______________: fired up or down _____ __________: In all cases: 1. d is _________________if the object ends up __________ the point where it started. 2. d is _________________if the object ends up __________ the point where it started. 3. v is positive if object is going ________________ 4. v is negative if object is going ________________ 5. a is _________________________ _________ down: up or right down or left always -9.81 m/s 2 …only for the time while it is ________________. in flight dropped fired thrown at an angle horizontally positive above negative below

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Ex 1: A ball is dropped. How far will it fall in 3.5 seconds? given: unknown: a = -9.81 m/s 2 v i = 0 t = 3.5 s d = ? equation: d = v i t + ½ a t 2 I.______________ motion A. Dropped Objects. Vertical d = 0t + ½(-9.81)(3.5) 2 d = ½(-9.81)(12.25) d = -60. m

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Ex. Harry Potter falls freely 99 meters from rest. How much time will he be in the air? given: unknown: a = -9.81 m/s 2 v i = 0 t = ? d = -99 m equation: d = v i t + ½ a t 2 -99 = 0t + ½(-9.81)(t) 2 -99 = -4.905t 2 t 2 = 20.2 t = 4.5 s

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Ex. A dinosaur falls off a cliff. What will be its velocity at the instant it hits ground if it falls for 1.3 seconds? given: unknown: equation: a = -9.81 m/s 2 v i = 0 t= 1.3 s v f = ? v f = v i + a t v f = 0 + (-9.81)(1.3) v f = -13 m/s A rock that has half the mass of the dinosaur is dropped at the same time. If it falls for the same time, what will its final speed be? Which will hit the ground first? same neither

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Ex. A ball is tossed up with an initial speed of 24 meters per second. How high up will it go? given: unknown: a = -9.81 m/s 2 v i = 24 m/s d= ? equation: v f = 0 vivi vfvf v f 2 = v i 2 + 2 a d What total distance will it travel before it lands? What will be its resultant displacement when it lands? 0 = 24 2 + 2(-9.81)d -576 = -19.6d 29.4 m = d 58.8 m 0. m B. Objects Fired Up or Down.

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For a ball fired or thrown straight up: going up coming down vivi 1._______ d each second on way up 2.______ d each second on way down 3. t up = _____________ 4. t total = _______ = __________ 5. v top =__________ 6. a top = __________ 7. speed up = _______________ 8.If object falls back to its original height, then: v f =______ t down less more 2t down 2t up -9.81 m/s 2 speed down -v i 0 v = 0 vfvf

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Ex. Mr. Butchko is fired directly up with an initial speed of 55 meters per second. How long will he be in the air? given: unknown: equation: a = -9.81 m/s 2 v i = 55 m/s t= ? v f = -55 m/s vivi vfvf a = Δv/t a = (v f – v i )/t -9.81 = (-55 – 55)/t t = (-110)/-9.81 t = 11 s How much time did he spend going up? t = 5.5 s

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Ex. A shot put is thrown straight down from a cliff with an initial speed of 15 m/s. How far must it fall before it reaches a speed of 35 m/s? given: unknown: equation: a = -9.81 m/s 2 v i = -15 m/s d= ? v f = -35 m/s v f 2 = v i 2 + 2 a d (-35) 2 = (-15) 2 + 2(-9.81)d 1225 - 225 = -19.6d -51 m = d 1000 = -19.6d 1000/(-19.6) = d

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Ex: ball dropped from rest v (m/s) t (s) t (s) d (m) v (m/s) a (m/s 2 ) 000-10 1 12 3 -20 -30 2 3 4 -10 -20 -10 -30 -10-40 -5 -20 -45 -80 5 m 15 m 25 m 35 m -10 m/s 2 C. Graphical analysis: use a ≈ _____________ -40

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total d 5 m 15 m 25 m 0 m 5 m 20 m 45 m time 0 s 1 s 2 s 3 s velocity 0 m/s -10 m/s -20 m/s -30 m/s See any patterns?

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Ball dropped: vectors vs. scalars v t v displacement distance d velocity speed acceleration acceleration d aa t t t t t ~ t 2 ~ t constant

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Stop here

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t (s) d (m) v (m/s) a (m/s 2 ) 0 -10 1 2 3 4 Ex: ball thrown straight up with v i = 30 m/s 5 6 -10 030

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10 v (m/s) t (s) 12 3 20 30 45 6 -30 -20 -10 5 m 15 m 25 m slope = ______________ throughout going up

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t (s) d (m) v (m/s) a (m/s 2 ) 0 0 -10 1 2 3 4 Ex: ball thrown straight up with v i = 30 m/s 5 6 -10 30 20 10 0 25 40 45

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10 v (m/s) t (s) 12 3 20 5 m 15 m 25 m 30 45 6 -30 -20 -10 5 m 15 m 25 m slope = ______________ throughout coming down going up

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t (s) d (m) v (m/s) a (m/s 2 ) 0 0 -10 1 2 3 4 Ex: ball thrown straight up with v i = 30 m/s 5 6 -10 30 20 10 0 25 40 45 -10 -20 -30 40 25 0

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10 v (m/s) t (s) 12 3 20 5 m 15 m 25 m 30 45 6 -30 -20 -10 5 m 15 m 25 m going up coming down positive d negative d top slope = ______________ throughout -10 m/s 2

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Going up: Going down: 5 m 15 m 25 m time 0 s 1 s 2 s 3 s v 0 30 20 10 0 v time 6 s 5 s 4 s 3 s time -10 -20 -30

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What will the graph of speed vs. time look like? At what time is the ball at its highest point? What are the v and a at that time? How do the the last 3 sec of this example compare to the example of a ball dropped from rest? 10 t (s) 12 3 20 30 45 6 t = v = a = 3.0 s 0 -10 m/s 2 the same

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10 v (m/s) t (s) 12 3 20 30 45 6 -30 -20 -10 Ex. How does the picture change if ball is thrown up a with different initial speed, say v i = 20 m/s?

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10 v (m/s) t (s) 12 3 20 30 45 6 -30 -20 -10 Ex. What if ball is thrown up with an initial speed v i = 10 m/s?

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10 v (m/s) t (s) 12 3 20 30 45 6 -30 -20 -10 Ex. What if thrown down a with speed v i = 10 m/s? Ball continues down until it strikes the ground.

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What remains the same in all of these graphs? acceleration = -9.8 m/s 2 Open your 3-ring binder to the Worksheet Table of Contents. Record the title of the worksheet: Free Fall WS

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d = v i t + ½ at 2 With v i = 0 and a = -10 d = 0t + ½ (-10)t 2 d = -5t 2 For t = 0, 1, 2, …. d = -5t 2 = -5(0 2 ) = 0 = -5(1 2 ) = -5 = -5(2 2 ) = -20 = -5(3 2 ) = -45 v f = v i + at With v i = 0 and a = -10 v f = -10t For t = 0, 1, 2, …. v f = 0 + (-10)t v f = -10t = -10(0) = 0 = -10(1) = -10 = -10(2) = -20 = -10(3) = -30 velocity: displacement:

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Aim: How can we approach projectile problems?

Aim: How can we approach projectile problems?

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